Solve similar triangles (advanced) khan academy

The pdf of the kth order statistic X(k) can be found using the formula: f(k)(x) = n!/[ (k-1)! (n-k)! ] * [ F(x) ]^(k-1) * [ 1-F(x) ]^(n-k) * f(x) where F(x) is the cdf of the uniform distribution on [0,8] and f(x) is the pdf of the uniform distribution, which is 1/8 for x in [0,8]. The expected value of X is 4.

Using this formula, we can find the pdf of X(k) for any k between 1 and n.

For the expected value of X, we can use the formula:

E[X] = ∫₀⁸ x * f(x) dx

Since X is uniformly distributed on [0,8], the pdf f(x) is constant over this interval, equal to 1/8. Therefore, we have:

E[X] = ∫₀⁸ x * (1/8) dx = 1/16 * x^2 |_₀⁸ = 4

So the expected value of X is 4.

Regarding the hint given, it seems to be unrelated to the problem at hand and does not provide any additional information for solving it.

Let X1, X2, ..., Xn denote independent and uniformly distributed random variables on the interval [0, 8]. To find the pdf of the kth order statistic, X(k), where k is an integer between 1 to n, we can use the following formula:

pdf of X(k) = (n! / [(k-1)! * (n-k)!]) * (x^(k-1) * (8-x)^(n-k)) / (8^n)

For the expected value E[X(k)], we can use the provided hint:

∫(x * pdf of X(k)) dx from 0 to 8 = ∫[x * (n! / [(k-1)! * (n-k)!]) * (x^(k-1) * (8-x)^(n-k)) / (8^n)] dx from 0 to 8

The hint suggests that the integral can be simplified using a gamma function Γ(a+) with unknown parameters a and β:

∫(x^4-4 * (1 - x)^β-1) dx = Γ(a)(β)

To find E[X(k)], solve the integral with the appropriate parameters for a and β.

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Yes , the density of pure water at standard temperature and pressure (STP) is  very close to 1 g/mL .

The density of water is defined as the measure of  mass per unit volume of water, which is the mass of water per unit volume of water, the density is  expressed in grams per milliliter (g/mL) or kilograms per cubic meter (kg/m³).

The density of pure water at standard temperature and pressure (STP) is =  1 g/mL, which is also equivalent to "1000 kg/m³" .

The density of water  vary slightly with the temperature and pressure.

For Example , at room temperature (about 20°C), the density of water is about 0.998 g/mL, which is slightly less than 1 g/mL .

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Answer:

41

Step-by-step explanation:

Usando BODMAS, entonces que tenemos

(2 + 4 * 3) =

(2 + 12) =

14

Con el segundo uno, tenemos

(3 * 2 - 2 * 2). Con esto, dices que

(3 * 2) - (2 * 2) =

6 - 4 =

2

Y ahora, decimos que

3 * (14) - 2(2) + 5 - 2 =

42 - 4 + 3 =

42 - 1 = 41

Nos respuesta a la pregunta es 41. Espero que tú entiendas

Answer:

I and IV only.

Step-by-step explanation:

There are 3 similar triangles in the diagram, so corresponding sides are in the same ratio. You can identify corresponding sides by checking that the angles opposite them are congruent.

Answer:

f-1(x)=x+1/3 is yr answer.

The number of waffles can be made from 15 eggs are, 20 waffles.

the waffles can be calculates as follows

4 cups of fluor + 6 eggs +2 tbsp oil = 8 waffles

we need 6 eggs to make 8 waffles

So, the waffles can we make from 15 eggs = \(\frac{8}{6} X 15 = 20\) waffles

Hence, the number of waffles can be made from 15 eggs are 20 waffles.

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Answer: 4

Step-by-step explanation:

2+2=4

Answer:

2 + 2 = 4

Step-by-step explanation:

If u just started to learn how to sum, you can use sticks

II + II = IIII

Since one side of a regular hexagon is extended to create an exterior angle, the measure of such exterior angle is: C. 60.

In Mathematics and Geometry, the sum of the interior angles of both a regular and irregular polygon is given by this formula:

Sum of interior angles = 180 × (n - 2)

Note: The given geometric figure (regular polygon) represents a hexagon and it has 6 sides.

Sum of interior angles = 180 × (6 - 2)

Sum of interior angles = 180 × 4

Sum of interior angles = 720°.

Each interior angle = 720/6 = 120°.

When the hexagon is extended create an exterior angle, its measure is given by;

x + 120 = 180°.

x = 180° - 120°

x = 60°.

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Answer:

x=2 , y= (-1/2)

Step-by-step explanation:

3x + 2y = 5
2x + 4y = 2

Consider Equation 1:- (3x+2y=5)

Multiply both sides by 2
2(3x + 2y) = 5*2
6x + 4y = 10

Subtract both equations-
6x + 4y =10
-2x + 4y =2

=> 4x =8
      x = 2

Substitute the value of x in equation 1

3*2 + 2y = 5
6 + 2y = 5
2y = 5-6
2y = (-1)

y = (-1/2)

Hope is helps ;)

Answer:

Step-by-step explanation:

24/x = 28/(32 - x)                  Cross multiply

24 * (32 - x) = 28x                 Remove the brackets.

768  - 24x = 28x                   Add 24x to both sides

768 = 28x + 24x

768 = 52x

52x = 768                              Divide by 52

x = 768/52

x = 14.77

AB = 32 - 14.77

AB = 17.23

Answer:

40: 56

Step-by-step explanation:

The tree diagram that summarizes these probabilities is Option (D).

Probability is the chance of occurrence of a certain event out of the total no. of events that can occur in a given context.

Here, N(S) = 10, The numbers from 0 - 9.

The probability of going to work by driving is (4/10) = 0.4.

If he drives, he has a probability of 0.1 of being late so P(NL) = 1 - 0.1 = 0.9.

The probability of going to work by walking is = 6/10 = 0.6.

if he walks, his probability of late rising to 0.25 so, P(NL) = 1 - 0.25 = 0.75.

Now we'll connect this information to the given options.

From the given options, Option (D) satisfies the given information.

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Answer:

D. 14.99d

Step-by-step explanation:

d represents the number of DVD's she purchased, and 14.99 was the cost for each DVD. Answer D is multiplying the variable d and the coefficient 14.99. When multiplying variables, there is no need to place a multiplication sign.

Answer:

C. 14.99 divided by d

Step-by-step explanation:

the answer is c because you don't know how many DVDs he bought so by dividing the answer you can then know the price of each DVD they bought.

Answer:

The answer is b.) hope this helps!!

Step-by-step explanation:

if you only look at H and H', you can see H' is being translated(slid) down the Y axis and since it is sliding down, it is -4, giving you (x, y-4)

Answer:

m = 4/3

Step-by-step explanation:

Step 1: Write equation

\(\frac{3m}{4} =\frac{4}{2}\)

Step 2: Solve for m

Answer:

2 2/3

Step-by-step explanation:

Since that you have to make the problem proportional, both sides of the inequality will have to be the same. 4/2 will have a total of 2, so what you need to do is multiply 3 by something in which divided by 4 will have a total of 2.

3 × 2 2/3 = 8. And 8/4 is 2, so that is proportional to 4/2.

The recursive formulas are NEXT = NOW – 8, starting at 50 and f(n + 1) = f(n) + 6.5, f(1) = 0

From the question, we have the following parameters that can be used in our computation:

The list of options

The general rule is that

A recursive formula is a function that derives it value from the previous term or terms

using the above as a guide, we have the following recursive formulas

NEXT = NOW – 8, starting at 50

f(n + 1) = f(n) + 6.5, f(1) = 0

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Answer:

I don't know the answer to this question

Three angles fit around a point, two of the angles are 115° and 53° , then the size of third angle would be 192° and it would be a reflex angle.

The sum of the angles around a point is 360 °

If the two angles are 115° and 53° , the sum of the two angles would be 168°

If we reduce the sum of the two angles from the total 360° , we get the size of third angle as 192°

As the size of third angle is more than 180° , so the name of the third angle is reflex angle because right angle is measured 90° , obtuse angle is measured more than 90° but less than 180° , reflex angle is measured more than 180° but less than 360° and acute angle is measured less than 90 °

Correct question is - Three angles fit around a point. Two of the angles are 115° and 53° . Work out the size of third angle and which of the words below describe the third angle

• Right angle

• Obtuse angle

• Reflex angle

• Acute angle

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A. The probability that one selected subcomponent is longer than 122 cm can be found by calculating the area under the normal distribution curve to the right of 122 cm. We can use the z-score formula to standardize the value and then look up the corresponding probability in the standard normal distribution table.

z = (122 - μ) / σ = (122 - 100) / 5.6 = 3.93 (approx.)

Looking up the corresponding probability for a z-score of 3.93 in the standard normal distribution table, we find that it is approximately 0.9999. Therefore, the probability that one selected subcomponent is longer than 122 cm is approximately 0.9999 or 99.99%.

B. To find the probability that the mean length of three randomly selected subcomponents exceeds 122 cm, we need to consider the distribution of the sample mean. Since the sample size is 3 and the subcomponent lengths are normally distributed, the distribution of the sample mean will also be normal.

The mean of the sample mean will still be the same as the population mean, which is 100 cm. However, the standard deviation of the sample mean (also known as the standard error) will be the population standard deviation divided by the square root of the sample size.

Standard error = σ / √n = 5.6 / √3 ≈ 3.24 cm

Now we can calculate the z-score for a mean length of 122 cm:

z = (122 - μ) / standard error = (122 - 100) / 3.24 ≈ 6.79 (approx.)

Again, looking up the corresponding probability for a z-score of 6.79 in the standard normal distribution table, we find that it is extremely close to 1. Therefore, the probability that the mean length of three randomly selected subcomponents exceeds 122 cm is very close to 1 or 100%.

C. If we want to find the probability that all three randomly selected subcomponents have lengths exceeding 122 cm, we can use the probability from Part A and raise it to the power of the sample size since we need all three subcomponents to satisfy the condition.

Probability = (0.9999)^3 ≈ 0.9997

Therefore, the probability that if three subcomponents are randomly selected, all three of them have lengths that exceed 122 cm is approximately 0.9997 or 99.97%.

Based on the given information about the normal distribution of subcomponent lengths, we calculated the probabilities for different scenarios. We found that the probability of selecting a subcomponent longer than 122 cm is very high at 99.99%. Similarly, the probability of the mean length of three subcomponents exceeding 122 cm is also very high at 100%. Finally, the probability that all three randomly selected subcomponents have lengths exceeding 122 cm is approximately 99.97%. These probabilities provide insights into the performance of the automatic machine in terms of producing longer subcomponents.

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Answer:

Step-by-step explanation:

You would use -6 and 7 to start your line. With the equation “y=5/6x+7", you would put a dot on 7. Then you would use the 5/6 to start making your line. With fractions, it's always rise/run. Starting from 7, you go up 5 then over(right) 6 until you run out of room on the graph. Then you do the opposite, down 5 then back(left) 6. Then you should have your first line. Then repeat that for the next equation. Start at -6, go down 4 and back three until you run out of room on the graph, then do the opposite. Go up 4 and over 3.

Let me know if this is confusing!

The domain of the vector function r(t) = (25 - t², e⁻³t, ln(t⁴)) is:

Domain: (-∞, 0) ∪ (0, +∞)

The domain of the vector function is determined by the domains of its component functions.

1. For the first component, 25 - t², there are no restrictions on the domain of t. It is defined for all real numbers.

2. For the second component, e⁻³t, the exponential function is defined for all real numbers, so there are no restrictions on the domain of t.

3. For the third component, ln(t⁴), the natural logarithm function is defined only for positive real numbers. Therefore, the expression t⁴ must be positive for ln(t⁴) to be defined. Since t⁴ is always non-negative (or zero), we only need to consider when t⁴ is positive.

t⁴ > 0

A fourth power of a real number is always positive except when the number is zero. Therefore, the expression t⁴ is positive for all values of t except t = 0.

In summary, the domain of the vector function r(t) = (25 - t², e⁻³t, ln(t⁴)) is:

Domain: (-∞, 0) ∪ (0, +∞)

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-5/-8

Step-by-step explanation:

I think the question is asking about the gradient so to find the gradient, you need to minus the first y coordinate form the second y coordinate

-4 - 1 = -5

then the first X from the second X

-6 - 2 = -8

Answer: -5=2x+11

Step-by-step explanation:

3x-5=5x+11

subtract 3x to both sides

3x-5 - 3x =5x+11 - 3x

simplify

-5 = 2x +11

answer is -5=2x+11

B) The length of GB is 3 in the given triangle.

The centroid of a triangle is the point at which the three medians of the triangle intersect. A median of a triangle is a line segment that connects a vertex of the triangle to the midpoint of the opposite side. The three medians divide the triangle into six smaller triangles, each with a vertex at the centroid.

The ratio in which the centroid divides a median of a triangle is 2:1. That is, the distance from the centroid to the vertex is twice the distance from the centroid to the midpoint of the opposite side.

So, if G is the centroid and B is the midpoint of the side opposite to point A, the ratio of EG: GB is 2:1.

so the length of GB = EG/2

so the length of GB = 3

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Complete question:

In ΔAEC, G is the centroid , as shown in the figure .

if EG = 6 ,find GB

A) 2

B) 3

C) 6

D) 9

The segment margin is obtained by deducting the traceable fixed costs of a segment from the segment's contribution margin is the correct answer.

In this question,

Segment margin is the amount of net profit or net loss generated by a portion of a business. Segment margin is the margin available after a segment has covered all of its costs. It’s one of the best ways to determine the long-term profitability of a segment.

i.e., Segment Margin = Segment’s Contribution Margin – Fixed Costs traced to the Segment

Contribution margin ratio is commonly expressed as a percentage of sales prices. Contribution margin is the amount remaining from sales revenue once all variable costs have been removed.

i.e., Contribution Margin = Sales Revenue – Variable Costs

Hence we can conclude that the segment margin is obtained by deducting the traceable fixed costs of a segment from the segment's contribution margin is the correct answer.

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Answer:

I think 13 cm. You add the numbers 5,5,3 together to get 13

Step-by-step explanation:

Answer:

25 cm

Step-by-step explanation:

Answer:

\( x = \frac{300}{b} \)

Step-by-step explanation:

We are given that, "b" number of buildings has 300 windows.

Let b represent the number of buildings.

Let x represent the number of windows per building.

Thus, the following equation can be used to expressed the number of windows for b buildings:

Number of buildings*number of windows per building = 300 windows

\( x*b = 300 \)

The number of windows each building has would be:

\( \frac{x*b}{b} = \frac{300}{b} \)

\( x = \frac{300}{b} \) windows per building